Method for generating control parameters from a response signal of a controlled system and system for adaptive setting of a PID controller

ABSTRACT

Setting parameters of a PID controller are obtained by feeding a step signal or another input signal to an assigned controlled system. The response signal emitted by the controlled system is sampled and the characteristics of the Bode diagram are generated from the input signal and the response signal by using a smoothing method and elementary correspondences. The characteristics are normalized and input values are derived therefrom for a neural network which is trained on the properties of the controlled systems. The neural network directly generates the setting parameters for the controller.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation of copending international applicationPCT/DE97/00242, filed on Feb. 7, 1997, which designated the UnitedStates.

BACKGROUND OF THE INVENTION

Field of the Invention

The invention relates to a method for generating control parameters froma response signal of a controlled system with a computer. It relates,further, to a system for adaptive setting of a PID controller with theaid of a neural network.

PID controllers are known from Otto Föllinger, “Regelungstechnik”[Control Technology], 5^(th) Ed., Hüttig Verlag, Heidelberg 1995, pages204-206. They are frequently used in process engineering. For thispurpose, the controllers must be calculated in order to be able tocontrol the assigned controlled system. In production engineering, thereare, as a rule, no models of the controlled system available forcalculating controllers. In order to set a PID controller, anidentification is frequently carried out which can be performed, forexample, offline on the basis of a measured step response. In thisprocess, the appropriate model with the associated model parameters issought from a given set of models of the controlled systems. A suitablePID controller can be calculated on the basis of this model.

It would be expedient if the identification step and the controllercalculation could be combined to form a single step. A well definedmapping of the step response onto the desired controller parameterswould result from this. In order to minimize the outlay arising in thiscase, it is obvious to approximate the same by means of a neuralnetwork. If such a trained neural network is available, suitablecontroller parameters can be found immediately by firstly recording thestep response of the controlled system of a given technical installationand then making it available to the neural network as input. The outputsof the neural network are the controller parameters being sought.

In order to train the neural network, it is possible to prescribecontrolled systems for which the associated controller parameters aredirectly known. It is possible to use, for example, an expert system forsetting PID controllers or a library of appropriate controllerparameters, which may be determined in some other way, as a basis fortraining the neural network. This device for training can be termed ateacher, for example. The task of the neural network is compared withthat of the teacher and the network weightings are corrected so as toreduce the output error of the neural network. This is performed for amultiplicity of different prescribed system models until the error issufficiently small for all the examples. Neural networks which satisfythese requirements are known, for example, from J. Hertz, A. Krogh, andR. Palmer, “Introduction to the Theory of Neural Computation”,Addison-Wesley Pub. Co., 1991, pages 115-147. A further solution isknown from international publication WO 93/12476. There, the controllerparameters are determined directly from the time signals with the aid ofthe neural network. As a rule such networks must be very large and aredifficult to train, and the emitted controller parameters are notreliable.

European patent disclosure EP 0 520 233 A2 discloses a device forindicating the parameters of a transmission system, in which asimulation module is used to compare estimated output signals withmeasured output signals. Deviations are minimized for optimumparameters.

Instead of the step response of the controlled system, the followingtext refers to the response signal of the controlled system.

SUMMARY OF THE INVENTION

It is accordingly an object of the invention to provide a method forgenerating control parameters from a response signal of a controlledsystem and a system for an adaptive setting of a PID controller with theaid of a neural network which overcomes the above-mentioneddisadvantages of the heretofore-known methods and systems of thisgeneral type and according to which, characteristics of a Bode diagramare generated from a noisy response signal, wherein the characteristicsare largely uninfluenced by the noise. A further object is to specify asystem for adaptively setting a PID controller with the aid of a neuralnetwork, in which the controller parameters emitted by the neuralnetwork ensure an acceptable controller setting even in the presence ofa noisy response signal.

With the foregoing and other objects in view there is provided, inaccordance with the invention, a method for generating controlparameters from a response signal of a controlled system with acomputer, the method which comprises:

sampling an input signal and a response signal for generating a sampledinput signal and a sampled response signal;

smoothing and optionally differentiating the sampled input signal andthe sampled response signal with the aid of a time-variant filter forgenerating a smoothed input signal and a smoothed response signal;

generating in each case frequency characteristics from the smoothedinput signal and the smoothed response signal;

forming a difference between the frequency characteristics in a Bodediagram; and

determining control parameters with the aid of the difference.

With the foregoing and other objects in view there is also provided, inaccordance with the invention, a method for generating controlparameters from a response signal of a controlled system with acomputer, the method which comprises:

sampling an input signal and a response signal for generating a sampledinput signal and a sampled response signal;

deconvoluting the response signal with respect to the input signal forgenerating a smoothed impulse response from the sampled response signal;

forming frequency characteristics in a Bode diagram from the impulseresponse; and

determining control parameters with the aid of the frequencycharacteristics.

With the foregoing and other objects in view there is furthermoreprovided, in accordance with the invention, a method for generatingcontrol parameters from a response signal of a controlled system with acomputer, the method which comprises:

sampling a response signal for generating a sampled response signal;

smoothing or smoothing and differentiating the sampled response signalwith the aid of a time-variant filter for generating a smoothed responsesignal;

generating frequency characteristics in a Bode diagram from the smoothedresponse signal;

determining control parameters with the aid of the frequencycharacteristics.

In preferred embodiments of the methods according to the invention anyof the steps of deconvoluting, smoothing or smoothing anddifferentiating of either the input signal or the response signal or thestep of generating the impulse response may be performed in accordancewith the formula:

{tilde over (x)}=Vx

v=V y

where y is a vector consisting of samples of the response signal, V is amatrix for at least one of deconvoluting, smoothing or smoothing anddifferentiating, v is a vector of a smoothed impulse response, x is avector of the input signal, and {tilde over (x)} is a vector of thesmoothed input signal.

In accordance with a further feature of the invention, the matrices Vfor smoothing, for smoothing and differentiating or for deconvolutingare obtained from an energy function having a term specifying adeviation of an approximation from a measured response signal, andhaving a term specifying a roughness of a reconstructed impulseresponse.

In accordance with a another feature of the invention, a smoothingdeconvolution matrix V is obtained by minimizing the following energyfunction:

ε( b )=k(( y−XA ³ b )^(T) D ₀( y−XA ³ b )+ v ^(T)

D ₁ v+a ^(T) D ₂ a+r ^(T) D ₃ r+b ^(T) D ₄ b )

where k denotes a constant, e.g. k=0.5, X a convolution integrationmatrix which is calculated as a function of the input signal x(t), A anintegration matrix, r=A b, a=A r, v=A a, and D ₀, D ₁ D ₂, . . . D ₄arbitrarily selectable diagonal matrices, and the solution of aminimization is

v=V y

V=A ³( A ^(3T) X ^(T) D ₀ XA ³ +A ^(3T) D ₁ A ³ +A ^(2T) D ₂ A ² +

A ^(T) D ₃ A+D ₄)⁻¹ A ^(3T) X ^(T) D ₀.

In accordance with a further feature of the invention, the matrix V forsmoothing or smoothing and differentiating is:

V+A ³( A ^(4T) D ₀ A ⁴ +A ^(3T) D ₁ A ³ +A ^(2T) D ₂ A ² +A ^(T) D ₃ A+D₄)⁻¹ A ^(4T) D ₀

where D ₁ . . . D ₄ denote arbitrarily selectable diagonal matrices, Aan integration matrix, and T a transposition.

In accordance with a further feature of the invention, the matrix forsmoothing or smoothing and differentiating is obtained from the energyfunction

ε( a )=k[( y−A ² a )^(T)( y−A ² a )+ a ^(T) Da]

the first term being the deviation of the approximation from themeasured response signal, the second term being the roughness of theapproximation, with s=Av, v=Aa, and s=A ² a, D being a diagonal matrix,A an integration matrix, k being a constant, e.g. k=0.5, y a vectorconsisting of samples of the response signal, and T indicating atransposition.

In accordance with a further feature of the invention, the matrix forsmoothing or the matrix for smoothing and differentiating is obtainedfrom the energy function

ε( b )=k[( y−A ⁴ b )^(T) D ₀( y−A ⁴ b )+ v ^(T) D ₁

v+a ^(T) D ₂ a+r ^(T) D ₃ r+b ^(T) D ₄ b ]

where D ₁ . . . D ₄ are diagonal matrices, A is an integration matrix,s=A v, v=A a, a=A r, r=A b, k is a constant, y a vector consisting ofsamples of the response signal, and T indicates a transposition.

In accordance with a further feature of the invention, the Bode diagramis normalized with respect to frequency and preferably normalized to afrequency at which a phase characteristic assumes a value −φ_(N).

In accordance with a further feature of the invention, characteristicsof the Bode diagram are generated in accordance with a method ofapproximating a step response or an impulse response by a polygon or byrectangular blocks and the transformation into the frequency domain isperformed with elementary correspondences.

In accordance with a further feature of the invention, a frequencyresponse is approximated with the aid of the relation:${H({j\omega})} \cong {\sum\limits_{v = 1}^{q}\quad {{h\left\lbrack {v - 1} \right\rbrack}{H_{v}({j\omega})}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}\quad {v_{v}{H_{v}({j\omega})}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively.

In accordance with a further feature of the invention, an approximationof the frequency response is obtained from the vector y with:$\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}\underset{\_}{{HV}_{y}}}$

with

H=[ h ₁ h ₂ . . . h _(m)]^(T),

and${\left\lbrack {{H\left( {j\omega}_{1} \right)}{H\left( {j\omega}_{2} \right)}\quad \ldots \quad {H\left( {j\omega}_{m} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\quad \ldots \quad {\underset{\_}{h}}_{m}} \right\rbrack}}},$

where f denotes an approximation of the frequency response, H afrequency transformation matrix, V a matrix for smoothing, for smoothingand differentiating or for deconvoluting, and y a vector consisting ofsamples of the response signal.

With the foregoing and other objects in view there is also provided, inaccordance with the invention, a system for adaptive setting of a PIDcontroller with the aid of a neural network, comprising:

a sampling device for sampling a response signal, the response signalemitted by a controlled system in response to a supplied input signal;

a transformation device for smoothing and optionally differentiating theinput signal and the response signal and transforming the input signaland the response signal into a frequency domain;

a diagram device for forming a difference between frequencycharacteristics of the input signal and the response signal in a Bodediagram and for generating a Bode diagram of the controlled system; and

a neural network for emitting parameters for setting a PID controller,an absolute value characteristic of the Bode diagram and a phasecharacteristic of the Bode diagram being supplied to the neural networkas input values either directly or after a conversion.

With the foregoing and other objects in view there is furthermoreprovided, in accordance with the invention, a system for adaptivesetting of a PID controller with the aid of a neural network,comprising:

a sampling device for sampling a response signal, the response signalemitted by a controlled system in response to a supplied input signal;

a deconvolution device for calculating a smoothed impulse response fromthe response signal as a function of the input signal;

a diagram device for obtaining a Bode diagram of the controlled systemfrom the smoothed impulse response;

a neural network for emitting parameters for setting a PID controller,an absolute value characteristic of the Bode diagram and a phasecharacteristic of the Bode diagram being supplied to the neural networkas input values either directly or after a conversion thereof.

With the foregoing and other objects in view there is also provided, inaccordance with the invention, a system for adaptive setting of a PIDcontroller with the aid of a neural network, comprising:

a sampling device for sampling a response signal, the response signalemitted by a controlled system in response to a supplied input signal;

a transformation device for smoothing and optionally differentiating theresponse signal and transforming the response signal into a frequencydomain;

a diagram device for generating a Bode diagram from the smoothedresponse signal;

a neural network for emitting parameters for setting a PID controller,an absolute value characteristic of the Bode diagram and a phasecharacteristic of the Bode diagram being supplied to the neural networkas input values either directly or after a conversion.

In accordance with a further feature of the invention, a normalizationdevice for normalizing the Bode diagram with respect to the frequency isprovided.

Preferred embodiments of the systems for the adaptive setting of a PIDcontroller operate by using the methods for generating controlparameters in accordance with the invention.

According to the invention, the controller parameters are not determinedby the neural network directly from the step response, but the frequencycharacteristics of the system are calculated in advance from the stepresponse. The neural network is then fed input values which arecalculated from the frequency characteristics of the system. As anadvantage, it is possible to use much smaller networks which emit goodcontroller parameters with greater reliability. Methods for calculatingthe frequency characteristics of the system from an emitted stepresponse are known, for example, from H. Unbehauen, “Regelungstechnik”[Control Technology], 1989, pages 370-389 and from R. Isermann,“Identifikation dynamischer Systeme 1” [Identification of DynamicSystems], Springer Verlag, 1989, pages 81-113. However, these becomeproblematic when noise signals are superimposed on the step response.When such a noisy step response is used to calculate the frequencycharacteristics which drive the neural network, it is still possiblethat the controller parameters generated by the neural network areunsuitable. The measures described by Unbehauen and Isemann forsmoothing the step response either require several measurements or arenot sufficient to achieve the desired reliability. For this reason, theinvention also describes a novel smoothing method which permits thefrequency characteristics of the system to be calculated from a singlenoisy measurement.

Consequently, the neural network does not receive as input variablesfeatures formed directly from the step response, but the step responseis preprocessed. This preprocessing comprises smoothing anddifferentiating the step response, followed by a Fourier transformation,which can be combined to form a matrix multiplication with acomplex-value matrix. The data thus obtained are plotted in the form ofa Bode diagram. Subsequently, the frequency characteristics found arenormalized, that is to say the absolute-value characteristic withrespect to the amplitude and the frequency, and the phase characteristicwith respect to the frequency. In the Bode diagram, this normalizationeffects a simple displacement of the frequency characteristics. Thenormalization quantity is that frequency at which the phasecharacteristic assumes the value −100°, and the associated absolutevalue of the absolute-value characteristic. The neural network musttherefore learn only normalized control parameters for normalizedsystems, which results in a simplification. Characteristic quantitiesare now formed as input variables for the neural network from theremaining normalized frequency characteristics. The output variables ofthe network represent the normalized controller parameters of the PIDcontroller. Finally, the desired controller parameters are obtained bydenormalization.

Several methods are known for obtaining frequency responses from a stepresponse of a linear controlled system. Reference is made to the methodsof the Fast Fourier Transform (FFT) or the Discrete Fourier Transform(DFT). A further practicable method is approximation of the stepresponse by means of a polygon and transformation into the frequencydomain by means of elementary correspondences, as is described by H.Unbehauen and R. Isermann for example. The direct application of thesemethods in the case of a noisy step response is, however, not sufficientas a rule for determining the control parameters. In this case, it isgenerally recommended to perform a time-consuming excitation of thecontrolled system by means of multiple steps or impulses or by means ofstochastic signals, which is seldom possible in process engineering.

In order to obtain sufficiently indicative frequency characteristics inthe Bode diagram for designing a PID controller with the aid of asingle, even noisy step response, according to the invention the stepresponse is firstly smoothed, use being made for the purpose ofsmoothing of the fact that the step response is available over theentire variation for the purpose of determining a point on the smoothedcurve. After the smoothing, the step response can be differentiated, theresult being an estimate of the system impulse response. The estimatedimpulse response now represents the basis for determining the frequencycharacteristics of the controlled system in a fashion analogous to themethods presented by Unbehauen and Isermann. This method still yieldsgood results even given a very noisy step response. The two namedoperations can be formulated in matrix notation and combined to form asingle matrix multiplication with a complex-value matrix.

The method has been described so far with the use of a step response.However, this is not necessary, since the method also operatessatisfactorily when an arbitrary response signal of a controlled systemis used.

In this case, there are two possibilities for generating the frequencycharacteristics in the case of a closed control loop. With the firstpossibility, the input signal and the response signal can be used. Withboth, the step response is firstly smoothed and then subjected toFourier transformation, as before. Differentiation can be dispensed withhere, having no influence on the result. The result is now two frequencycharacteristics, one for the input signal and one for the responsesignal. The difference between the two frequency characteristics in theBode diagram yields the desired frequency response of the system. Thispossibility is likewise described by Unbehauen and Isermann.

With the second possibility, the smoothed impulse response of the systemis calculated by deconvoluting the response signal with respect to theinput signal. This deconvolution operation depends on the input signal.If the input signal is stepped, the deconvolution operation is identicalto a smoothing and subsequent differentiation. The second method thusrepresents a generalization of the smoothing method as a smoothingdeconvolution.

Other features which are considered as characteristic for the inventionare set forth in the appended claims.

Although the invention is illustrated and described herein as embodiedin a method for generating control parameters from a response signal ofa controlled system with a computer and as a system for an adaptivesetting of a PID controller with the aid of a neural network, it isnevertheless not intended to be limited to the details shown, sincevarious modifications and structural changes may be made therein withoutdeparting from the spirit of the invention and within the scope andrange of equivalents of the claims.

The construction and method of operation of the invention, however,together with additional objects and advantages thereof will be bestunderstood from the following description of specific embodiments whenread in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic a block diagram of the system,

FIG. 2 is a schematic of a detailed part of the system,

FIG. 3 is a schematic of the system with an open control loop,

FIG. 4a is a schematic of the system with a closed control loop for thefirst method,

FIG. 4b is a schematic of the system with a closed control loop for thedeconvolution method,

FIG. 5 is a graph of a noisy step response,

FIG. 6 is a graph of the course of the absolute-value characteristic,and

FIG. 7 is a graph of the course of the phase characteristic.

In the further description the step response, which is emitted by thecontrolled system in the case of the presence of a step signal, is used.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the figures of the drawings in detail and first,particularly, to FIG. 1, there is seen the design of a control loopcomprising a controlled system RS and a controller RG. The controller RGmay indicate a PID controller. The controlled system RS is representedonce more symbolically, and here the invention provides that a stepsignal SS be fed, the controlled system generating on the basis of thestep signal a step response SA, whose amplitude y is represented plottedagainst time t. Before a neural network NN can generate parameters Kp,Tn, Tv for setting the controller RG, it must firstly be trained. Here,Tn is the integral-action time, Tv the derivative-action time and Kp theproportionality factor (see also Otto Föllinger, Regelungstechnik, 5.Auflage, Hüttingverlag, Heidelberg 1995, pages 204-206).

The neural network NN is trained with the aid of a teacher LR which, inaccordance with one of the methods specified above, sets the weightingsof the neural network such that the values emitted by the teacher LR andthe neural network on the basis of a step response are approximatelyidentical. For this purpose, the neural network NN must be fed the stepresponse SA for a large number of different systems. The teacher LR isgenerally fed the system parameters directly. However, other variablescan also be processed for the purpose of uniquely characterizing thesystem. As long as the values of the neural network NN deviate fromthose of the teacher, the teacher adjusts the weightings of the neuralnetwork NN until no further reduction in the deviation is possible. Thetraining of the neural network NN is not the subject matter of thepresent invention; it can be performed in a known way.

A detailed representation of the system follows from FIG. 2. The stepresponse SA is sampled at different times, the sampling times T₁, T₂ . .. T_(q), and the amplitude values y present at these instants are fed toa means for smoothing and Fourier transformation M. In one step, thelatter carries out the inventive smoothing of the step response SA and,using the methods specified by H. Unbehauen and R. Isermann, generatesthe amplitude characteristic y1 and the phase characteristic y2 from thesmoothed step response. The two characteristics of the Bode diagram arerepresented in FIG. 2 as a function of the frequency ω. The twocharacteristics are normalized in a normalization unit NE, andcharacteristic quantities, for example C, D, E, F, which are fed to theneural network NN as input variables, are formed from the normalizedcharacteristics. The characteristic quantity G is calculated directlyfrom the step response and likewise fed to the neural network NN. Theneural network NN generates the controller parameters Kp, Tn, Tv on thebasis of these input variables. These controller parameters Kp, Tn, Tvare used to set the PID controller in such a way that the control loopoperates satisfactorily.

It will firstly be explained below how a smoothed step response isgenerated from the noisy step response SA. Use is made in this processof the fact that in the normal case the step response of a givencontrolled system changes relatively sluggishly in time. Rapid changesare to be ascribed with high probability to noise signals. To simplifythe representation of the invention, the measured step response y(t) isassumed to have q equidistant interpolation points, that is to say

y[n]=y(nT), n=0,1, . . . , q−1

Here, T is the sampling time. The time-discrete signal y(n) can now becombined to form a vector $\begin{matrix}{\underset{\_}{y} = \begin{bmatrix}{y\lbrack 0\rbrack} \\{y\lbrack 1\rbrack} \\\vdots \\{y\left\lbrack {q - 1} \right\rbrack}\end{bmatrix}} & (1)\end{matrix}$

Furthermore, the (q×q) summation matrix is introduced, $\begin{matrix}{\underset{\_}{A}:={\frac{200}{q - 1}\begin{bmatrix}1 & 0 & \cdots & 0 \\1 & 1 & \cdots & 0 \\\vdots & \vdots & \cdots & \vdots \\1 & 1 & \cdots & 1\end{bmatrix}}} & (2)\end{matrix}$

by means of which it is possible, for example, to express by Ay anaccumulating summation of the components of y. This represents one ofmany possible approximations of the integration operator $\begin{matrix}{{A\left\{ y \right\}}:={\frac{200}{\left( {q - 1} \right)T}\begin{bmatrix}{\int_{0}^{0}{{y(T)}\quad {T}}} \\{\int_{0}^{T}{{y(T)}\quad {T}}} \\\vdots \\{\int_{0}^{{({q - 1})}T}{{y(T)}\quad {T}}}\end{bmatrix}}} & \left( {2a} \right)\end{matrix}$

The aim is to find a smoothed vector s as approximation for the vectory. Use is made for this purpose of the smoothing effect of theaccumulating summation, that is to say the vector s is firstly expressedby

s=A v   (3)

v=A a   (4)

The condition s=y would then signify A ² a=y, something which causes theroughness in y to appear amplified for a. An attempt is then made to setup approximately the equality between s and y, the aim then being, forexample, for ∥a∥ or, with a suitably prescribed diagonal matrix D withpositive entries, for the expression a ^(T) Da to be as small aspossible. This constitutes the basic idea of the smoothing method. Theenergy function

ε( a )=k[( y−A ² a )^(T)( y−A ² a )+ a ^(T) Da]  (5)

k=constant, for example k=0.5

is formed and minimized to obtain a solution. Here, the first termevaluates the deviation of the approximation from the measured stepresponse, and the second term evaluates the roughness of theapproximation. The solution

a=[ A ^(2T) A ² +D] ⁻¹ A ^(2T) y   (6)

is calculated by equating the gradient of ε(a) to zero, and from thisthe vector s for the smoothed step response is calculated in accordancewith equations (3) and (4). In the limiting case of D=0, this gives s=y,that is to say the smoothing effect disappears.

The noise suppression can be further improved by including yet furtherterms of the same type in equations (3) and (4) and supplementing theenergy function equation (5) in this regard. The following energyfunction

 ε( b )=k[( y−A ⁴ b )^(T) D ₀( y−A ⁴ b )+ v ^(T)

D ₁ v+a ^(T) D ₂ a+r ^(T) D ₃ r+b ^(T) D ₄ b ]  (7)

is advantageous and which has suitably selected diagonal matrices D ₀, D₁, D ₂, D ₃ and D ₄ with positive entries, the following equations (8)and (9)

a=Ar   (8)

r=Ab   (9)

being added to equations (3) and (4). The matrix D ₁ is set as a rule inthis case to 0.

The importance of the novel smoothing method for the subsequent furtherprocessing resides, above all, in the possibility of also directlyspecifying from the noisy step response y(t) via the vector v a good,satisfactorily smooth estimate for the impulse response h(t)=ds(t)/dtusing $\begin{matrix}{{h({nT})} = {{h\lbrack n\rbrack} \cong {v_{n + 1}/{T\left( {q - 1} \right)}}}} & (10)\end{matrix}$

v_(n+1) denoting the (n+1)th component of v and s(t) the exact stepresponse SA-U without noise. These relationships follow from FIG. 5,which shows the noisy step response SA-G, the noiseless step responseSA-U and the smoothed step response SA-R. The reconstruction of theimpulse response can be performed using

ν=V _(y)   (11)

by means of a simple matrix multiplication of the vector y by a fixedmatrix, V being determined in the way described by minimizing the energyfunction equation (7), substituting it in equations (9), (8) and (4),resolving it for v and extracting y from the brackets. The result for Vis

V=A ³ [A ^(4T) D ₀ A ⁴ +A ^(3T) D ₁ A ³ +A ^(2T) D ₂ A ² +A ^(T) D ₃ A+D₄]⁻¹ A ^(4T) D ₀  (12)

The method described can now be supplemented for the case when the inputsignal is not stepped. The convolution operator $\begin{matrix}{{X\left\{ v \right\}}:={\frac{200}{\left( {q - 1} \right)T}\begin{bmatrix}{\int_{0}^{0}{{x\left( {t - \tau} \right)}{v(\tau)}\quad {\tau}}} \\{\int_{0}^{T}{{x\left( {t - \tau} \right)}{v(\tau)}{\tau}}} \\\vdots \\{\int_{0}^{{({q - 1})}T}{{y\left( {t - \tau} \right)}{v(\tau)}\quad {\tau}}}\end{bmatrix}}} & \left( {12a} \right)\end{matrix}$

is introduced for this purpose. By contrast with A{v}, X{v} denotes aconvolution integration operator of v(t) with the input signal x(t).Just as in the case of A{ }, it is possible from this to form aconvolution matrix X by approximating the integration with a sum.

The smoothed impulse response is now determined not by minimizing theenergy function equation (7), but by minimizing the extended energyfunction

ε( b )=k(( y−XA ³ b )^(T) D ₀( y−XA ³

b)+ν ^(T) D ₁ ν+a ^(T) D ₂ a+r ^(T)

D ₃ r+b ^(T) D ₄ b )  (12b)

The solution is now obtained as

v=Vy   (12c)

where

V=A ³( A ^(3T) X ^(T) D ₀ X A ³ +A ^(3T) D ₁

A ³ +A ^(2T) D ₂ A ² +A ^(T) D ₃ A+D ₄)⁻¹ A ^(3T) X ^(T) D ₀  (12e)

The vector characterizing the impulse response can thus be determined,as in the case of the stepped excitation by customary matrixmultiplication, from the vector y of the measured output signal. Thematrix V is, however, now a function of the input signal x(t), becausethe matrix X depends on the input signal.

The calculation of the Bode diagram from the smoothed impulse responseis performed analogously in accordance with the methods presented by H.Unbehauen and R. Isermann on the basis of a polygon for the stepresponse. This is advantageous because the frequency points are often tolie equidistantly on the logarithmic scale. However, in the case of themethod employed only a single impulse response is used, although afterpreliminary smoothing and differentiation of the step response emittedby the controlled system. This is necessary in process engineering,since a step response, for example in the case of chemical plants,frequently requires several hours, and for reasons of safety it isgenerally desirable to deviate the system as little as possible from theoperating point, that is to say it is impossible in many instances tohave a sequence of several steps or a high-frequency excitation.

The calculation of the system frequency response is explained in moredetail below. The desired frequency response H(jω), 0<ω<∞ is obtained byLaplace transformation of the impulse response h(t)=ds(t)/dt of thesystem, the generally complex-valued Laplace variable s being set equalto jω. As an approximation, the impulse response h(t) can beapproximated by a stair-step function, the ν-th rectangular block(ν=1,2, . . . , q−1) in each case having the width T and the heighth(ν-1)=h((ν−1)T)≅v_(ν)/T. Only the last, qth block of height h[q−1]embraces the time interval ((q−1)T,∞). This corresponds in the result tothe method represented in by H. Unbehauen and R. Isermann. Anapproximation by means of a polygon connection or by splines is alsopossible for the purpose of increasing the accuracy.

The frequency responses of the individual rectangular blocks can bespecified directly by means of elementary correspondences (see e.g. thepublications of H. Unbehauen and R. Isermann). If H_(ν)(jω) denotes thefrequency response of the νth rectangular block normalized to height 1,the sum $\begin{matrix}{{H({j\omega})} \cong {\sum\limits_{v = 1}^{q}\quad {{h\left\lbrack {v - 1} \right\rbrack}{H_{v}({j\omega})}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}\quad {v_{v}{H_{v}({j\omega})}}}}} & (13)\end{matrix}$

is obtained as the approximation of the desired frequency responseH(jω).

An essential fact concerning the above consideration is that in the caseof a fixed frequency ω=ω_(μ) in the above sum, the contributionsH_(ν)(jω) of each individual block normalized to height 1 arecharacterized in each case by one fixed complex number. If these complexnumbers are combined to form a vector, that is to say $\begin{matrix}{{\underset{\_}{h}}_{\mu} = \begin{bmatrix}{H_{1}\left( {j\omega}_{\mu} \right)} \\{H_{2}\left( {j\omega}_{\mu} \right)} \\\vdots \\{H_{q}\left( {j\omega}_{\mu} \right)}\end{bmatrix}} & (14)\end{matrix}$

the result is $\begin{matrix}{{H({j\omega})} \cong {\frac{1}{\left( {q - 1} \right)T}{\underset{\_}{v}}^{T}{\underset{\_}{h}}_{\mu}}} & (15)\end{matrix}$

or, in the case of several, arbitrary frequency points ω₁, ω₂ . . .ω_(m), correspondingly, $\begin{matrix}{\left\lbrack {{H\left( {j\omega}_{1} \right)}{H\left( {j\omega}_{2} \right)}\quad \ldots \quad {H\left( {j\omega}_{m} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\quad \ldots {\underset{\_}{h}}_{m}} \right\rbrack}}} & (16)\end{matrix}$

This means that calculation of the frequency response can beapproximated by the matrix multiplication of the vector v of the impulseresponse and a fixed matrix.

It is assumed in this case that the starting point is not the samplevalues of the measured step response, but the already smoothed vector vof the impulse response. Since it is also the case with the smoothingalgorithm that the vector v is yielded from the vector y of the measuredsample values by multiplication with a fixed matrix, the two matrixmultiplications can be combined so that no additional effort resultsfrom the smoothing.

Using summary notation with the abbreviations $\begin{matrix}{\underset{\_}{f} = \begin{bmatrix}{H\left( {j\omega}_{1} \right)} \\{H\left( {j\omega}_{2} \right)} \\\vdots \\{H\left( {j\omega}_{m} \right)}\end{bmatrix}} & (17)\end{matrix}$

the frequency transformation matrix

H:=[h ₁ h ₂ . . . h _(m)]^(T)  (18)

and the smoothing matrix V as solution matrix of the previouslydescribed smoothing method, the solution $\begin{matrix}{\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}\underset{\_}{{HV}_{y}}}} & (19)\end{matrix}$

is therefore obtained immediately as the approximation of the systemfrequency response from the vector y of the measured sample values ofthe system step response.

As already set forth in the introduction, the frequency characteristicsshown in FIGS. 6, 7 can therefore be obtained directly by matrixmultiplications of the vector y by a fixed matrix calculated once inadvance.

The normalized values can be obtained in the following way from thesefrequency characteristics (see FIG. 6, FIG. 7):

Let x=log 10(ωT) denote the logarithmic frequency, b(x) theabsolute-value characteristic and p(x) the phase characteristic in theBode diagram (see FIGS. 6, 7). These functions are now firstly smoothed,that is to say the functions {tilde over (b)}(x), and {tilde over(p)}(x), are formed. The point x₀ where

{tilde over (p)}(x ₀)=−φ_(N)

is now sought. φ_(N) is here a constant, for example φ_(N)=100. Thefeature B is thus

B=x _(o)

The feature A is obtained from the amplitude characteristic inaccordance with

A={tilde over (b)}(x ₀)

The normalized functions

b _(n)(x _(N)):=b(x _(N) +x ₀)−A=b(x _(N) +B)−A  (20)

and

p _(N)(x _(N)):=p(x _(N) +x ₀)=p(x _(N) +B)  (21)

are now formed.

Three further characteristic qunatities are calculated, specificallyusing $\begin{matrix}{{f_{c}\left( x_{N} \right)} = {{\frac{1}{90}{\int_{0}^{x_{N}}{{p_{N}(\theta)}\quad {\theta}}}} - {b_{N}\left( x_{N} \right)}}} & (22)\end{matrix}$

 C=f _(c)(0.16)−f _(c)(−0.84)  (23)

E=b _(N)(0)  (24)

 F=p _(N)(0)+φ_(N)  (25)

$\begin{matrix}{D = {{\log \quad 10\left( {\int_{0.0244}^{25}{10^{2{B_{N}{(\theta)}}}\quad {\theta}}} \right)} - {2E}}} & (26)\end{matrix}$

where

B_(N)(θ):=b_(N)(log 10(θ))

The feature G is calculated from the response signal y(t) by estimatingthe noise amplitude, that is to say using

y(t)=y _(g)(t)+n(t)r

where

y_(g) is the smoothed response signal,

n(t) is the noise with signal power 1, and

r is the noise amplitude,

it holds approximately that

G=r.

It is assumed in this case that the input signal has the mean signalpower 1. If the signal power of the input signal is not 1, G is dividedby the root of the signal power.

The feature C permits systems of minimum phase and non-minimum phase tobe distinguished. The feature D can also be denoted as the spectralenergy of the impulse response. The feature G serves the purpose ofdetermining more careful controller parameters in the case of a noisyresponse signal. The finally trained neural network, comprising threeinput neurons, 4 hidden neurons and three output neurons generatestherefrom three output variables c, d and e, from which the desiredcontroller parameters can be calculated in accordance with

K _(p)10^(c−A)

T _(n)=10^(d−B)

T _(v)=10^(e−B).

The steps for calculating the frequency characteristics will now beexplained with the aid of FIGS. 3 and 4a, 4 b: As FIG. 3 shows, tocalculate the characteristics in the Bode diagram it is possible tostart from a controlled system which can be fed a step signal (opencontrol loop). It then suffices merely to measure the step response,since the step signal is known.

In the case of control loops, for example in process engineering, it isoften impossible for the controlled system to be driven directly. It isthen possible, for example, for the closed control loop to be fed thestep signal in order then to be able to measure the input signal and theresponse signal of the controlled system to determine the frequencycharacteristics. An example of this is to be gathered in FIG. 4a andFIG. 4b. It may be seen from FIG. 4a that after transformation into thefrequency domain, the difference between the frequency responses of theinput signal and the response signal is formed and used to generate thecharacteristics. The explanations above relate to the first method.

It may be seen from FIG. 4b that for the second method the impulseresponse is calculated by a deconvolution operation which depends on theinput signal X(t). It is then not necessary to smooth the input andresponse signals. A smooth impulse response is emitted by theconvolution method presented even in the case of a noisy measurement.The Bode diagram required is obtained therefrom by Fouriertransformation using known methods as described by Unbehauen andIsermann.

I claim:
 1. A method for generating control parameters from a responsesignal of a controlled system with a computer, the method whichcomprises: sampling an input signal and a response signal for generatinga sampled input signal and a sampled response signal; smoothing thesampled input signal and the sampled response signal with the aid of atime-variant filter for generating a smoothed input signal and asmoothed response signal by smoothing at least one of the sampled inputsignal and the sampled response signal in accordance with the formula:{tilde over (x)}=Vx v=V y where y denotes a vector consisting of samplesof the response signal, V a matrix for smoothing, v a vector of asmoothed impulse response, x a vector of the input signal, and {tildeover (x)} a vector of the smoothed input signal; generating in each casefrequency characteristics from the smoothed input signal and thesmoothed response signal; forming a difference between the frequencycharacteristics in a Bode diagram; and determining control parameterswith the aid of the difference.
 2. The method according to claim 1,which comprises: differentiating the smoothed input signal and thesmoothed response signal for generating a smoothed and differentiatedinput signal and a smoothed and differentiated response signal with theaid of the time-variant filter; and generating the frequencycharacteristics from the smoothed and differentiated input signal andthe smoothed and differentiated response signal.
 3. The method accordingto claim 1, which comprises normalizing the Bode diagram with respect tofrequency.
 4. The method according to claim 1, which comprises:generating characteristics of the Bode diagram in accordance with amethod of approximating one of a step response and an impulse responseby one of a polygon and rectangular blocks; and transforming into afrequency domain with elementary correspondences.
 5. The methodaccording to claim 1, which comprises obtaining the matrix V forsmoothing from an energy function having a term specifying a deviationof an approximation from a measured response signal, and having a termspecifying a roughness of a reconstructed impulse response.
 6. A methodfor generating control parameters from a response signal of a controlledsystem with a computer, which comprises: sampling an input signal and aresponse signal for generating a sampled input signal and a sampledresponse signal; smoothing the sampled input signal and the sampledresponse signal with the aid of a time-variant filter for generating asmoothed input signal and a smoothed response signal; generating in eachcase frequency characteristics from the smoothed input signal and thesmoothed response signal; forming a difference between the frequencycharacteristics in a Bode diagram; determining control parameters withthe aid of the difference; normalizing the Bode diagram with respect toa frequency at which a phase characteristic assumes a value −φ_(N).
 7. Amethod for generating control parameters from a response signal of acontrolled system with a computer, which comprises: sampling an inputsignal and a response signal for generating a sampled input signal and asampled response signal; smoothing the sampled input signal and thesampled response signal with the aid of a time-variant filter forgenerating a smooth input signal and a smoothed response signal;generating in each case frequency characteristics from the smoothedinput signal and the smoothed response signal; forming a differencebetween the frequency characteristics in a Bode diagram by approximatingone of a step response and an impulse response by one of a polygon andrectangular blocks; determining control parameters with the aid of thedifference; transforming into a frequency domain with elementarycorrespondences; and approximating a frequency response with the aid ofa relation:${H\left( {j\quad \omega} \right)} \cong {\sum\limits_{v = 1}^{q}{{h\left\lbrack {v - 1} \right\rbrack}{H_{v}\left( {j\quad \omega} \right)}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}{v_{v}{H_{v}\left( {j\quad \omega} \right)}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively.
 8. A method forgenerating control parameters from a response signal of a controlledsystem with a computer, which comprises: sampling an input signal and aresponse signal for generating a sampled input signal and a sampledresponse signal; smoothing the sampled input signal and the sampledresponse signal with the aid of a time-variant filter for generating asmoothed input signal and a smoothed response signal; generating in eachcase frequency characteristics from the smoothed input signal and thesmoothed response signal; forming a difference between the frequencycharacteristics in a Bode diagram; normalizing the Bode diagram to afrequency at which a phase characteristic assumes a value −φ_(N);determining control parameters with the aid of the difference;differentiating the smoothed input signal and the smoothed responsesignal for generating a smoothed and differentiated input signal and asmoothed and differentiated response signal with the aid of thetime-variant filter; and generating the frequency characteristics fromthe smoothed and differentiated input signal and the smoothed anddifferentiated response signal.
 9. A method for generating controlparameters from a response signal of a controlled system with acomputer, which comprises: sampling an input signal and a responsesignal for generating a sampled input signal and a sampled responsesignal; smoothing the sampled input signal and the sampled responsesignal with the aid of a time-variant filter for generating a smoothedinput signal and a smoothed response signal; generating in each casefrequency characteristics from the smoothed input signal and thesmoothed response signal; forming a difference between the frequencycharacteristics in a Bode diagram in accordance with a method ofapproximating one of a step response and an impulse response by one of apolygon and rectangular blocks which comprises approximating a frequencyresponse with the aid of a relation:${H\left( {j\quad \omega} \right)} \cong {\sum\limits_{v = 1}^{q}{{h\left\lbrack {v - 1} \right\rbrack}{H_{v}\left( {j\quad \omega} \right)}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}{v_{v}{H_{v}\left( {j\quad \omega} \right)}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively; determining controlparameters with the aid of the difference; differentiating the smoothedinput signal and the smoothed response signal for generating a smoothedand differentiated input signal and a smoothed and differentiatedresponse signal with the aid of the time-variant filter; generating thefrequency characteristics from the smoothed and differentiated inputsignal and the smoothed and differentiated response signal; andtransforming into a frequency domain with elementary correspondences.10. The method according to claim 5, wherein the matrix V for smoothingis: V=A ³( A ^(4T) D ₀ A ⁴ +A ^(3T) D ₁ A ³ +A ^(2T) D ₂ A ² +A ^(T) D ₃A+D ₄)⁻¹ A ^(4T) D ₀ where D ₁ . . . D ₄ denote arbitrarily selectablediagonal matrices, A an integration matrix, and T a transposition. 11.The method according to claim 7, which comprises obtaining anapproximation of the frequency response from the vector y with:$\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}\underset{\_}{H}\underset{\_}{V}\underset{\_}{y}}$

with H=[h ₁ h ₂ . . . h _(m)]^(T), and${\left\lbrack {{H\left( {j\quad \omega_{1}} \right)}{H\left( {j\quad \omega_{2}} \right)}\quad \ldots \quad {H\left( {j\quad \omega_{m}} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\ldots {\underset{\_}{h}}_{m}} \right\rbrack}}},$

where f denotes an approximation of the frequency response, H afrequency transformation matrix, V a matrix for smoothing, and y avector consisting of samples of the response signal.
 12. The methodaccording to claim 11, wherein the matrix V for smoothing anddifferentiating is: V=A ³( A ^(4T) D ₀ A ⁴ +A ^(3T) D ₁ A ³ +A ^(2T) D ₂A ² +A ^(T) D ₃ A+D ₄)⁻¹ A ^(4T) D ₀ where D ₁ . . . D ₄ denotearbitrarily selectable diagonal matrices, A an integration matrix, and Ta transposition.
 13. The method according to claim 9, which comprisesobtaining an approximation of the frequency response from the vector ywith:$\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}\underset{\_}{H}\underset{\_}{V}\underset{\_}{y}}$

with H=[h ₁ h ₂ . . . h _(m)]^(T), and${\left\lbrack {{H\left( {j\quad \omega_{1}} \right)}{H\left( {j\quad \omega_{2}} \right)}\quad \ldots \quad {H\left( {j\quad \omega_{m}} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\ldots {\underset{\_}{h}}_{m}} \right\rbrack}}},$

where f denotes an approximation of the frequency response, H afrequency transformation matrix, V a matrix for smoothing anddifferentiating, and y a vector consisting of samples of the responsesignal.
 14. A method for generating control parameters from a responsesignal of a controlled system with a computer, which comprises: samplingan input signal and a response signal for generating a sampled inputsignal and a sampled response signal; deconvoluting the response signalwith respect to the input signal for generating a smoothed impulseresponse from the sampled response signal in accordance with theformula: {tilde over (x)}=Vx v=V y where y denotes a vector consistingof samples of the response signal, V a matrix for deconvolution, v avector of a smoothed impulse response, x a vector of the input signal,and {tilde over (x)} a vector of a smoothed input signal; formingfrequency characteristics in a Bode diagram from the impulse response;and determining control parameters with the aid of the frequencycharacteristics.
 15. The method according to claim 14, which comprisesobtaining the matrix for deconvolution from an energy function which hasa term which specifying the deviation of the approximation from ameasured response signal, and having a term specifying a roughness of areconstructed impulse response.
 16. A method for generating controlparameters from a response signal of a controlled system with acomputer, which comprises: sampling an input signal and a responsesignal for generating a sampled input signal and a sampled responsesignal; deconvoluting the response signal with respect to the inputsignal for generating a smoothed impulse response from the sampledresponse signal; forming frequency characteristics in a Bode diagramfrom the impulse response; normalizing the Bode diagram to a frequencyat which a phase characteristic assumes a value −φ_(N); and determiningcontrol parameters with the aid of the frequency characteristics. 17.The method according to claim 15, wherein the matrix V for deconvolutionis obtained by minimizing the following energy function: ε( b )=k(( y−XA³ b )^(T) D ₀( y−X A ³ b )+ v ^(T) D ₁ v+a ^(TD) ₂ a +r ^(T) D ₃ r+b^(T) D ₄ b ) where k denotes a constant, X a convolution integrationmatrix which is calculated as a function of the input signal x(t), A anintegration matrix, r=A b, a=A r, v=A a, and D ₀, D ₁, D ₂, . . . D ₄arbitrarily selectable diagonal matrices, and the solution of aminimization is v=V y V=A ³( A ^(3T) X ^(T) D ₀ X A ³ +A ^(3T) D ₁ A ³ +A ^(2T) D ₂ A ² +A ^(T) D ₃ A+D ₄)⁻¹ A ^(3T) X ^(T) D ₀.
 18. A methodfor generating control parameters from a response signal of a controlledsystem with a computer, which comprises: sampling an input signal and aresponse signal for generating a sampled input signal and a sampledresponse signal; deconvoluting the response signal with respect to theinput signal for generating a smoothed impulse response from the sampledresponse signal; forming frequency characteristics in a Bode diagramfrom the impulse response; and generating characteristics of the Bodediagram in accordance with a method of approximating one of a stepresponse and an impulse response by one of a polygon and rectangularblocks; transforming into a frequency domain with elementarycorrespondences; determining control parameters with the aid of thefrequency characteristics; and approximating a frequency response withthe aid of a relation:${H\left( {j\quad \omega} \right)} \cong {\sum\limits_{v = 1}^{q}{{h\left\lbrack {v - 1} \right\rbrack}{H_{v}\left( {j\quad \omega} \right)}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}{v_{v}{H_{v}\left( {j\quad \omega} \right)}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively.
 19. The methodaccording to claim 17, wherein the constant k has a value of 0.5. 20.The method according to claim 18, which comprises obtaining anapproximation of the frequency response from the vector y with:$\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}\underset{\_}{H}\underset{\_}{V}\underset{\_}{y}}$

with H[h ₁ h ₂ . . . h _(m)]^(T), and${\left\lbrack {{H\left( {j\quad \omega_{1}} \right)}{H\left( {j\quad \omega_{2}} \right)}\quad \ldots \quad {H\left( {j\quad \omega_{m}} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\ldots {\underset{\_}{h}}_{m}} \right\rbrack}}},$

where f denotes an approximation of the frequency response, H afrequency transformation matrix, V a matrix for smoothing anddifferentiating, and y a vector consisting of samples of the responsesignal.
 21. A method for generating control parameters from a responsesignal of a controlled system with a computer, the method whichcomprises: sampling a response signal for generating a sampled responsesignal; smoothing the sampled response signal with the aid of atime-variant filter for generating a smoothed response signal;generating frequency characteristics in a Bode diagram from the smoothedresponse signal; determining control parameters with the aid of thefrequency characteristics.
 22. The method according to claim 21, whichcomprises: differentiating the smoothed response signal for generating asmoothed and differentiated response signal with the aid of thetime-variant filter; and generating the frequency characteristics fromthe smoothed and differentiated response signal.
 23. The methodaccording to claim 21, which comprises normalizing the Bode diagram withrespect to frequency.
 24. The method according to claim 21, whichcomprises: generating characteristics of the Bode diagram in accordancewith a method of approximating one of a step response and an impulseresponse by one of a polygon and rectangular blocks; and transforminginto a frequency domain with elementary correspondences.
 25. The methodaccording to claim 22, wherein the smoothing and the differentiating ofthe response signal are performed in accordance with the formula: {tildeover (x)}=Vx v=V y where y denotes a vector consisting of samples of theresponse signal, V a matrix for smoothing and differentiating, v avector a smoothed impulse response, x a vector of an input signal, and{tilde over (x)} is a vector of a smoothed input signal.
 26. The methodaccording to claim 22, which comprises normalizing the Bode diagram withrespect to frequency.
 27. The method according to claim 22, whichcomprises: generating characteristics of the Bode diagram in accordancewith a method of approximating one of a step response and an impulseresponse by one of a polygon and rectangular blocks; and transforminginto a frequency domain with elementary correspondences.
 28. The methodaccording to claim 21, which comprises obtaining the matrix V forsmoothing from an energy function having a term specifying a deviationof an approximation from a measured response signal, and having a termspecifying a roughness of a reconstructed impulse response.
 29. A methodfor generating control parameters from a response signal of a controlledsystem with a computer, which comprises: sampling a response signal forgenerating a sampled response signal; smoothing the sampled responsesignal with the aid of a time-variant filter for generating a smoothedresponse signal; generating frequency characteristics in a Bode diagramfrom the smoothed response signal; determining control parameters withthe aid of the frequency characteristics; and normalizing the Bodediagram with respect to a frequency at which a phase characteristicassumes a value −φ_(N).
 30. A method for generating control parametersfrom a response signal of a controlled system with a computer, whichcomprises: sampling a response signal for generating a sampled responsesignal; smoothing the sampled response signal with the aid of atime-variant filter for generating a smoothed response signal;generating frequency characteristics in a Bode diagram from the smoothedresponse signal; determining control parameters with the aid of thefrequency characteristics; generating characteristics of the Bodediagram in accordance with a method of approximating one of a stepresponse and an impulse response by one of a polygon and rectangularblocks; and transforming into a frequency domain with elementarycorrespondences; and approximating a frequency response with the aid ofa relation:${H\left( {j\quad \omega} \right)} \cong {\sum\limits_{v = 1}^{q}{{h\left\lbrack {v - 1} \right\rbrack}{H_{v}\left( {j\quad \omega} \right)}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}{v_{v}{H_{v}\left( {j\quad \omega} \right)}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively.
 31. The methodaccording to claim 25, which comprises obtaining the matrix V forsmoothing and differentiating from an energy function having a termspecifying a deviation of an approximation from a measured responsesignal, and having a term specifying a roughness of a reconstructedimpulse response.
 32. The method according to claim 26, which comprisesnormalizing to a frequency at which a phase characteristic assumes avalue −φ_(N).
 33. The method according to claim 27, which comprisesapproximating a frequency response with the aid of a relation:${H({j\omega})}\quad \cong {\sum\limits_{v = 1}^{q}\quad {{h\left\lbrack {v - 1} \right\rbrack}{H_{v}\left( {j\quad \omega} \right)}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}\quad {v_{v}{H_{v}\left( {j\quad \omega} \right)}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively.
 34. The methodaccording to claim 28, which comprises obtaining the matrix forsmoothing from the energy function  ε( a )=k[( y−A ² a )^(T)( y−A ² a )+a ^(T) Da] the first term being the deviation of the approximation fromthe measured response signal, the second term being the roughness of theapproximation, with s=Av, v=Aa, and s=A ² a, D being a diagonal matrix,A an integration matrix, k a constant, y a vector consisting of samplesof the response signal, and T indicating a transposition.
 35. The methodaccording to claim 28, which comprises obtaining the matrix forsmoothing from the energy function ε( b )=k[( y−A ⁴ b )^(T) D ₀( y−A ⁴ b)+ v ^(T) D ₁ v+a ^(T) D ₂ a+r ^(T) D ₃ r+b ^(T) D ₄ b ] where D ₁ . . .D ₄ are diagonal matrices, A is an integration matrix, s=A v, v=A a, a=Ar, r=A b, k is a constant, y a vector consisting of samples of theresponse signal, and T indicates a transposition.
 36. The methodaccording to claim 30, which comprises obtaining an approximation of thefrequency response from the vector y with:$\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}\underset{\_}{H}\underset{\_}{V}\underset{\_}{y}}$

with H=[h ₁ h ₂ . . . h _(m)]^(T), and${\left\lbrack {{H\left( {j\quad \omega_{1}} \right)}{H\left( {j\quad \omega_{2}} \right)}\quad \ldots \quad {H\left( {j\quad \omega_{m}} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\ldots {\underset{\_}{h}}_{m}} \right\rbrack}}},$

where f denotes an approximation of the frequency response, H afrequency transformation matrix, V a matrix for smoothing, and y avector consisting of samples of the response signal.
 37. A method forgenerating control parameters from a response signal of a controlledsystem with a computer, which comprises: sampling a response signal forgenerating a sampled response signal; smoothing the sampled responsesignal with the aid of a time-variant filter for generating a smoothedresponse signalin accordance with the formula: {tilde over (x)}=Vx v=V ywhere y denotes a vector consisting of samples of the response signal, Va matrix for smoothing and differentiating, v a vector a smoothedimpulse response, x a vector of an input signal, and {tilde over (x)} isa vector of a smoothed input signal; generating frequencycharacteristics in a Bode diagram from the smoothed response signal;determining control parameters with the aid of the frequencycharacteristics; differentiating the smoothed response signal forgenerating a smoothed and differentiated response signal with the aid ofthe time-variant filter; generating the frequency characteristics fromthe smoothed and differentiated response signal; obtaining the matrixfor smoothing and differentiating from the energy function ε( a )=k[(y−A ² a )^(T)( y−A ² a )+ a ^(T) Da] the first term being the deviationof the approximation from the measured response signal, the second termbeing the roughness of the approximation, with s=Av, v=Aa, and s=A ² a,D being a diagonal matrix, A an integration matrix, k being a constant,y a vector consisting of samples of the response signal, and Tindicating a transposition.
 38. A method for generating controlparameters from a response signal of a controlled system with acomputer, which comprises: sampling a response signal for generating asampled response signal; smoothing the sampled response signal with theaid of a time-variant filter for generating a smoothed response signalin accordance with the formula: {tilde over (x)}=Vx v=V y where ydenotes a vector consisting of samples of the response signal, V amatrix for smoothing and differentiating, v a vector a smoothed impulseresponse, x a vector of an input signal, and {tilde over (x)} is avector of a smoothed input signal; generating frequency characteristicsin a Bode diagram from the smoothed response signal; determining controlparameters with the aid of the frequency characteristics;differentiating the smoothed response signal for generating a smoothedand differentiated response signal with the aid of the time-variantfilter; generating the frequency characteristics from the smoothed anddifferentiated response signal; obtaining the matrix for smoothing anddifferentiating from the energy function ε( b )=k[( y−A ⁴ b )^(T) D ₀(y−A ⁴ b)+ v ^(T) D ₁ v+a ^(T) D ₂ a+r ^(T) D ₃ r+b ^(T) D ₄ b] where D ₁. . . D₄ are diagonal matrices, A is an integration matrix, s=A v, v=Aa, a=A r, r=A b, k is a constant, y a vector consisting of samples ofthe response signal, and T indicates a transposition.
 39. A method forgenerating control parameters from a response signal of a controlledsystem with a computer, which comprises: sampling a response signal forgenerating a sampled response signal; smoothing the sampled responsesignal with the aid of a time-variant filter for generating a smoothedresponse signal; generating frequency characteristics in a Bode diagramfrom the smoothed response signal; determining control parameters withthe aid of the frequency characteristics; differentiating the smoothedresponse signal for generating a smoothed and differentiated responsesignal with the aid of the time-variant filter; generating the frequencycharacteristics from the smoothed and differentiated response signal;generating characteristics of the Bode diagram in accordance with amethod of approximating one of a step response and an impulse responseby one of a polygon and rectangular blocks; transforming into afrequency domain with elementary correspondences; approximating afrequency response with the aid of a relation:${H({j\omega})}\quad \cong {\sum\limits_{v = 1}^{q}\quad {{h\left\lbrack {v - 1} \right\rbrack}{H_{v}\left( {j\quad \omega} \right)}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}\quad {v_{v}{H_{v}\left( {j\quad \omega} \right)}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively; and obtaining anapproximation of the frequency response from the vector y with:$\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}{\underset{\_}{HV}}_{\underset{\_}{y}}}$

with H=[h ₁ h ₂ . . . h _(m)]^(T), and [H(jω ₁)H(jω ₂) . . . H(jω_(m))]≅${\left\lbrack {{H\left( {j\quad \omega_{1}} \right)}{H\left( {j\quad \omega_{2}} \right)}\quad \cdots \quad {H\left( {j\quad \omega_{m}} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\quad \cdots \quad {\underset{\_}{h}}_{m}} \right\rbrack}}},$

  v ^(T) [h ₁ h ₂ . . . h _(m)], where f denotes an approximation of thefrequency response, H a frequency transformation matrix, V a matrix forsmoothing and differentiating, and y a vector consisting of samples ofthe response signal.
 40. The method according to claim 34, wherein theconstant k has a value of 0.5.
 41. The method according to claim 37,wherein the constant k has a value of 0.5.
 42. A system for adaptivesetting of a PID controller with the aid of a neural network,comprising: a sampling device for sampling a response signal, theresponse signal emitted by a controlled system in response to a suppliedinput signal; a transformation device for smoothing the input signal andthe response signal and transforming the input signal and the responsesignal into a frequency domain, said transformation device performingthe smoothing of the input signal and the response signal in accordancewith the formula: {tilde over (x)}=Vx v=V y where y denotes a vectorconsisting of samples of the response signal, V a matrix for smoothing,v a vector of a smoothed impulse response, x a vector of the inputsignal, and {tilde over (x)} a vector of the smoothed input signal; adiagram device for forming a difference between frequencycharacteristics of the input signal and the response signal in a Bodediagram and for generating a Bode diagram of the controlled system; anda neural network for emitting parameters for setting a PID controller,an absolute value characteristic of the Bode diagram and a phasecharacteristic of the Bode diagram being supplied to said neural networkas input values.
 43. The system according to claim 42, wherein saidtransformation device additionally differentiates the input signal andthe response signal.
 44. The system according to claim 42, wherein saidneural network is supplied with the absolute value characteristic of theBode diagram and the phase characteristic of the Bode diagram after aconversion thereof.
 45. The system according to claim 42, including anormalization device for normalizing the Bode diagram with respect tofrequency.
 46. The system according to claim 42, wherein said diagramdevice generates the characteristics of the Bode diagram in accordancewith a method of approximating one of a step response and an impulseresponse by one of a polygon and rectangular blocks, and performs atransformation into the frequency domain with elementarycorrespondences.
 47. A system for adaptive setting of a PID controllerwith the aid of a neural network, comprising: a sampling device forsampling a response signal, the response signal emitted by a controlledsystem in response to a supplied input signal; a transformation devicefor smoothing the input signal and the response signal and transformingthe input signal and the response signal into a frequency domain; adiagram device for forming a difference between frequencycharacteristics of the input signal and the response signal in a Bodediagram and for generating a Bode diagram of the controlled system; aneural network for emitting parameters for setting a PID controller, anabsolute value characteristic of the Bode diagram and a phasecharacteristic of the Bode diagram being supplied to said neural networkas input values; a normalization device for normalizing the Bode diagramwith respect to frequency, said normalization unit performing anormalization to a frequency at which the phase characteristic assumes avalue −φ_(N).
 48. The system according to claim 42, wherein saidtransformation device obtains the matrix V for smoothing from an energyfunction having a term specifying a deviation of an approximation from ameasured response signal, and having a term specifying a roughness of areconstructed impulse response.
 49. A system for adaptive setting of aPID controller with the aid of a neural network, comprising: a samplingdevice for sampling a response signal, the response signal emitted by acontrolled system in response to a supplied input signal; atransformation device for smoothing the input signal and the responsesignal and transforming the input signal and the response signal into afrequency domain; a diagram device for forming a difference betweenfrequency characteristics of the input signal and the response signal ina Bode diagram and for generating a Bode diagram of the controlledsystem; and a neural network for emitting parameters for setting a PIDcontroller, an absolute value characteristic of the Bode diagram and aphase characteristic of the Bode diagram being supplied to said neuralnetwork as input values; said diagram device generating thecharacteristics of the Bode diagram in accordance with a method ofapproximating one of a step response and an impulse response by one of apolygon and rectangular blocks, and performs a transformation into thefrequency domain with elementary correspondences and said diagram deviceapproximating a frequency response with the aid of a relation:${H\left( {j\quad \omega} \right)} \cong {\sum\limits_{v = 1}^{q}{{h\left\lbrack {v - 1} \right\rbrack}{H_{v}\left( {j\quad \omega} \right)}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}{v_{v}{H_{v}\left( {j\quad \omega} \right)}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively.
 50. The systemaccording to claim 48, wherein said transformation device uses thematrix V for smoothing: V=A ³( A ^(4T) D ₀ A ⁴ +A ^(3T) D ₁ A ³ +A ^(2T)D ₂ A ² +A ^(T) D ₃ A+D ₄)⁻¹ A ^(4T) D ₀ where D ₁ . . . D ₄ denotearbitrarily selectable diagonal matrices, A an integration matrix, and Ta transposition.
 51. The system according to claim 49, wherein saiddiagram device obtains an approximation of the frequency response from avector y with:$\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}\underset{\_}{H}\underset{\_}{V}\underset{\_}{y}}$

with   H=[h ₁ h ₂ . . . h _(m)]^(T), and${\left\lbrack {{H\left( {j\quad \omega_{1}} \right)}{H\left( {j\quad \omega_{2}} \right)}\quad \ldots \quad {H\left( {j\quad \omega_{m}} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\ldots {\underset{\_}{h}}_{m}} \right\rbrack}}},$

where f denotes an approximation of the frequency response, H afrequency transformation matrix, V a matrix for smoothing, and y avector consisting of samples of the response signal.
 52. A system foradaptive setting of a PID controller with the aid of a neural network,comprising: a sampling device for sampling a response signal, theresponse signal emitted by a controlled system in response to a suppliedinput signal; a deconvolution device for calculating a smoothed impulseresponse from the response signal as a function of the input signal,said deconvolution device performing the smoothing of the responsesignal in accordance with the formula: {tilde over (x)}=Vx v=V y where ydenotes a vector consisting of samples of the response signal, V amatrix for deconvoluting, v a vector of a smoothed impulse response, x avector of the input signal, and {tilde over (x)} a vector of a smoothedinput signal; a diagram de vice f or obtaining a Bode diagram of thecontrolled system from the smoothed impulse response; and a neuralnetwork for emitting parameters for setting a PID controller, anabsolute value characteristic of the Bode diagram and a phasecharacteristic of the Bode diagram being supplied to said neural networkas input values.
 53. The system according to claim 52, wherein saidneural network is supplied with the absolute value characteristic of theBode diagram and the phase characteristic of the Bode diagram after aconversion thereof.
 54. The system according to claim 52, whichcomprises a normalization device for normalizing the Bode diagram withrespect to the frequency.
 55. The system according to claim 52, whereinsaid diagram device generates the characteristics of the Bode diagram inaccordance with a method of approximating one of a step response and animpulse response by one of a polygon and rectangular blocks, andperforms a transformation into the frequency domain with elementarycorrespondences.
 56. A system for adaptive setting of a PID controllerwith the aid of a neural network, comprising: a sampling device forsampling a response signal, the response signal emitted by a controlledsystem in response to a supplied input signal; a deconvolution devicefor calculating a smoothed impulse response from the response signal asa function of the input signal; a diagram device for obtaining a Bodediagram of the controlled system from the smoothed impulse response; aneural network for emitting parameters for setting a PID controller, anabsolute value characteristic of the Bode diagram and a phasecharacteristic of the Bode diagram being supplied to said neural networkas input values; a normalization device for normalizing the Bode diagramwith respect to the frequency, said normalization device performing anormalization to a frequency at which the phase characteristic assumes avalue −φ_(N).
 57. The system according to claim 52, wherein saidtransformation device obtains the matrix V for deconvoluting from anenergy function having a term specifying a deviation of an approximationfrom a measured response signal, and having a term specifying aroughness of a reconstructed impulse response.
 58. A system for adaptivesetting of a PID controller with the aid of a neural network,comprising: a sampling device for sampling a response signal, theresponse signal emitted by a controlled system in response to a suppliedinput signal; a deconvolution device for calculating a smoothed impulseresponse from the response signal as a function of the input signal; adiagram device for obtaining a Bode diagram of the controlled systemfrom the smoothed impulse response, said diagram device generating thecharacteristics of the Bode diagram in accordance with a method ofapproximating one of a step response and an impulse response by one of apolygon and rectangular blocks, and performs a transformation into thefrequency domain with elementary correspondences and approximating afrequency response with the aid of a relation:${H({j\omega})} \cong {\sum\limits_{v = 1}^{q}\quad {{h\left\lbrack {v - 1} \right\rbrack}{H_{v}({j\omega})}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}\quad {v_{v}{H_{v}({j\omega})}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively; and a neural networkfor emitting parameters for setting a PID controller, an absolute valuecharacteristic of the Bode diagram and a phase characteristic of theBode diagram being supplied to said neural network as input values. 59.The system according to claim 57, wherein said transformation deviceobtains the matrix V for deconvoluting by minimizing the followingenergy function: ε( b )=k(( y−XA ³ b )^(T) D ₀( y−X A ³ b )+ v ^(T) D ₁+a ^(T) D ₂ a+r ^(T) D ₃ r+b ^(T) D ₄ b ) where k denotes a constant, Xa convolution integration matrix which is calculated as a function ofthe input signal x(t), A an integration matrix, r=A b, a=A r, v=A a, andD ₀, D ₁, D ₂, . . . D ₄ arbitrarily selectable diagonal matrices, andthe solution of a minimization is v=V y V=A ³( A ^(3T) X ^(T) D ₀ X A ³+A ^(3T) D ₁ A ³ A ^(2T) D ₂ A ² +A ^(T) D ₃ A+D ₄)⁻¹ A ^(3T) X ^(T) D₀.
 60. The system according to claim 58, wherein said diagram deviceobtains an approximation of a frequency response from a vector y with:$\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}\underset{\_}{H}\underset{\_}{V}\underset{\_}{y}}$

with H=[h ₁ h ₂ . . . h _(m)]^(T), and${\left\lbrack {{H\left( {j\quad \omega_{1}} \right)}{H\left( {j\quad \omega_{2}} \right)}\quad \ldots \quad {H\left( {j\quad \omega_{m}} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\ldots {\underset{\_}{h}}_{m}} \right\rbrack}}},$

where f denotes an approximation of the frequency response, H afrequency transformation matrix, V a matrix for at least one ofsmoothing and deconvoluting, and y a vector consisting of samples of theresponse signal.
 61. A system for adaptive setting of a PID controllerwith the aid of a neural network, comprising: a sampling device forsampling a response signal, the response signal emitted by a controlledsystem in response to a supplied input signal; a transformation devicefor smoothing the response signal and transforming the response signalinto a frequency domain, said transformation device performs thesmoothing of the response signal in accordance with the formula: {tildeover (x)}=Vx v=V y where y denotes a vector consisting of samples of theresponse signal, V a matrix for at least one of smoothing anddifferentiating, v a vector of a smoothed impulse response, x a vectorof the input signal, and {tilde over (x)} a vector of a smoothed inputsignal; a diagram device for generating a Bode diagram from a smoothedresponse signal; a neural network for emitting parameters for setting aPID controller, an absolute value characteristic of the Bode diagram anda phase characteristic of the Bode diagram being supplied to said neuralnetwork as input values.
 62. The system according to claim 61, whereinsaid transformation device additionally differentiates the responsesignal.
 63. The system according to claim 61, wherein said neuralnetwork is supplied with the absolute value characteristic of the Bodediagram and the phase characteristic of the Bode diagram after aconversion thereof.
 64. The system according to claim 61, including anormalization device for normalizing the Bode diagram with respect tofrequency.
 65. The system according to claim 61, wherein said diagramdevice generates the characteristics of the Bode diagram in accordancewith a method of approximating one of a step response and an impulseresponse by one of a polygon and rectangular blocks, and performs thetransformation into a frequency domain with elementary correspondences.66. The system according to claim 61, wherein said transformation deviceobtains the matrix V for at least one of smoothing and differentiatingfrom an energy function having a term specifying a deviation of anapproximation from a measured response signal, and having a termspecifying a roughness of a reconstructed impulse response.
 67. A systemfor adaptive setting of a PID controller with the aid of a neuralnetwork, comprising: a sampling device for sampling a response signal,the response signal emitted by a controlled system in response to asupplied input signal; a transformation device for smoothing theresponse signal and transforming the response signal into a frequencydomain; a diagram device for generating a Bode diagram from a smoothedresponse signal and generating the characteristics of the Bode diagramin accordance with a method of approximating one of a step response andan impulse response by one of a polygon and rectangular blocks, andperforms the transformation into a frequency domain with elementarycorrespondences, and approximating a frequency response with the aid ofa relation:${H({j\omega})} \cong {\sum\limits_{v = 1}^{q}\quad {{h\left\lbrack {v - 1} \right\rbrack}{H_{v}({j\omega})}}} \cong {\frac{1}{\left( {q - 1} \right)T}{\sum\limits_{v = 1}^{q}\quad {v_{v}{H_{v}({j\omega})}}}}$

where H(jω) denotes a frequency response, and h and T symbolize a heightand a width of a rectangular block, respectively; and a neural networkfor emitting parameters for setting a PID controller, an absolute valuecharacteristic of the Bode diagram and a phase characteristic of theBode diagram being supplied to said neural network as input values. 68.The system according to claim 67, wherein said diagram device obtains anapproximation of the frequency response from a vector y with:$\underset{\_}{f} \cong {\frac{1}{\left( {q - 1} \right)T}\underset{\_}{H}\underset{\_}{V}\underset{\_}{y}}$

with H=[h ₁ h ₂ . . . h _(m)]^(T), and${\left\lbrack {{H\left( {j\quad \omega_{1}} \right)}{H\left( {j\quad \omega_{2}} \right)}\quad \ldots \quad {H\left( {j\quad \omega_{m}} \right)}} \right\rbrack \cong {\frac{1}{\left( {q - 1} \right)T}{{\underset{\_}{v}}^{T}\left\lbrack {{\underset{\_}{h}}_{1}{\underset{\_}{h}}_{2}\ldots {\underset{\_}{h}}_{m}} \right\rbrack}}},$

where f denotes an approximation of the frequency response, H afrequency transformation matrix, V a matrix for at least one ofsmoothing and differentiating, and y a vector consisting of samples ofthe response signal.